1. Preheat oven to 400°. Sprinkle chicken with salt, pepper, and paprika.
2. Heat oil in a 12-inch cast-iron skillet over high heat until oil just begins to smoke.
3. Place chicken in skillet, skin sides down; reduce heat to medium-high, and cook 15 minutes. Transfer chicken to a plate; discard drippings.
4. Cut lemon into 1/4-inch-thick rounds. Stir together olives, caperberries, almonds, and wine in skillet; add lemon slices. Place chicken, skin sides up, in skillet.
5. Bake at 400° for 25 to 30 minutes. Sprinkle with parsley.